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A girl ran to the top of some stairs - AQA - GCSE Physics - Question 2 - 2022 - Paper 1

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A girl ran to the top of some stairs. Figure 2 shows the stairs. The height of the stairs was 1.7 m. The mass of the girl was 50 kg. gravitational field strength = ... show full transcript

Worked Solution & Example Answer:A girl ran to the top of some stairs - AQA - GCSE Physics - Question 2 - 2022 - Paper 1

Step 1

Calculate the change in gravitational potential energy of the girl.

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Answer

To calculate the gravitational potential energy (E_p) of the girl, we use the formula:

Ep=extmassimesextgravitationalfieldstrengthimesextheightE_p = ext{mass} imes ext{gravitational field strength} imes ext{height}

Substituting the provided values:

  • Mass = 50 kg
  • Gravitational field strength = 9.8 N/kg
  • Height = 1.7 m

Thus:

Ep=50imes9.8imes1.7E_p = 50 imes 9.8 imes 1.7

Calculating this gives:

Ep=833extJE_p = 833 ext{ J}

Step 2

Calculate the power of the boy.

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Answer

To find the power (P) of the boy, we use the formula:

P=work donetimeP = \frac{\text{work done}}{\text{time}}

Given:

  • Work done = 1800 J
  • Time = 1.44 s

We can substitute the values into the formula:

P=18001.44P = \frac{1800}{1.44}

Calculating this yields:

P=1250extWP = 1250 ext{ W}

Step 3

Calculate the kinetic energy of the boy at the top of the stairs.

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Answer

To calculate the kinetic energy (E_k) of the boy, we use the equation:

Ek=0.5×mass×(extspeed)2E_k = 0.5 \times \text{mass} \times ( ext{speed})^2

Substituting the values:

  • Mass = 70 kg
  • Speed = 2.0 m/s

Thus:

Ek=0.5×70×(2.0)2E_k = 0.5 \times 70 \times (2.0)^2

Calculating gives:

Ek=140extJE_k = 140 ext{ J}

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